Noncommutative localisation in algebraic K-theory II

In [Amnon Neeman, Andrew Ranicki, Noncommutative localisation in algebraic K-theory I, Geom. Topol. 8 (2004) 1385-1425] we proved a localisation theorem in the algebraic K-theory of noncommutative rings. The main purpose of the current article is to express the general theorem of the previous paper in a more user-friendly fashion, in a way more suitable for applications. In the process we compare our result to the existing theorems in the literature, showing how the previous paper improves all the existing results.It should be pointed out that there have been two very interesting recent preprints on related topics. The reader is referred to the beautiful papers of Krause [Henning Krause, Cohomological quotients and smashing localizations, http://wwwmath.upb.de/~hkrause/publications.html. [8]] and Dwyer [William G. Dwyer, Noncommutative localization in homotopy theory, preprint, http://www.nd.edu/~wgd/. [4]]. Krause studies the lifting of chain complexes and the relation with the telescope conjecture, and Dwyer generalises to the homotopy theoretic framework.     

Mass transfer and benzene removal from air using latex rubber tubing and a hollow-fiber membrane module

A dense-phase latex rubber tube and a polyporous propylene hollow-fiber membrane module (HFMM) were investigated for control of benzene-contaminated gas streams. The abiotic mass flux observed through the latex tube was 3.9–13 mg/(min·m²) for 150 ppm of benzene at various gas and liquid flow rates, while a 100-fold lower mass flux was observed in the HFMM. After seeding with an aromatic-degrading culture enriched from activated sludge, the observed removal was 80% of 150 ppm, corresponding toa mass flux of 45 mg/(min·m²). The observed mass flux through the HFMM during biofiltration also rose, to 0.4 mg/(min·m²). Because the HFMM had a 50-fold higher surface area than the latex tube, the observed ben zene removal was 99.8%. Compared to conventional biofilters, the two reactors had modest elimination capacities, 2.5–18 g/(m³·h) in the latex tube membrane bioreactor and 4.8–58 g/(m³·h) in the HFMM. Although the HFMM had a higher elimination capacity, the gas-phase pressure drop was much greater.     

Anomalous proximity effect in gold coated (110) YBa2Cu3O7-delta films: penetration of the Andreev bound states

Scanning tunneling spectroscopy of (110)YBa(2)Cu(3)O(7-delta)/Au bilayers reveal a proximity effect markedly different from the conventional one. While proximity-induced mini-gaps rarely appear in the Au layer, the Andreev bound states clearly penetrate into the metal. Zero bias conductance peaks are measured on Au layers thinner than 7 nm with a magnitude similar to those detected on the bare superconductor films. The peaks then decay abruptly with Au thickness and disappear above 10 nm. This length is shorter than the normal coherence length and corresponds to the (ballistic) mean free path.     

Excited-state intermolecular proton transfer of firefly luciferin III. Proton transfer to a mild base

Steady-state and time-resolved techniques were employed to study the excited-state proton transfer (ESPT) from d-luciferin, the natural substrate of the firefly luciferase, to the mild acetate base in aqueous solutions. We found that in 1 M aqueous solutions of acetate or higher, a proton transfer (PT) process to the acetate takes place within 30 ps in both H(2)O and D(2)O solutions. The time-resolved emission signal is composed of three components. We found that the short-time component decay time is 300 and 600 fs in H(2)O and D(2)O, respectively. This component is attributed either to a PT process via the shortest water bridged complex available, ROH··H(2)O··Ac(-), or to PT taking place within a contact ion pair. The second time component of 2000 and 3000 fs for H(2)O and D(2)O, respectively, is attributed to ROH* acetate complex, whose proton wire is longer by one water molecule. The decay rate of the third, long-time component is proportional to the acetate concentration. We attribute it to the diffusion-assisted reaction as well as to PT process to the solvent.     

Stabilizing stick-slip friction

Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we show, experimentally and theoretically, that the stick-slip periods synchronize. We further show that this phase locking is related to the inhibition of slow rupture modes which forces a transition to fast rupture, providing a possible mechanism for observed remote triggering of earthquakes. Such manipulation of collective modes may be generally relevant to extended nonlinear systems driven near to criticality.     

A cardinal preserving extension making the set of points of countable V cofinality nonstationary

Assuming large cardinals we produce a forcing extension of V which preserves cardinals, does not add reals, and makes the set of points of countable V cofinality in κ⁺ nonstationary. Continuing to force further, we obtain an extension in which the set of points of countable V cofinality in ν is nonstationary for every regular ν ≥ κ⁺. Finally we show that our large cardinal assumption is optimal. This material is based upon work supported by the National Science Foundation under Grant no. DMS-0094174.     

The connection between a conjecture of Carlisle and Kropholler,now a theorem of Benson and Crawley-Boevey,and Grothendieck's Riemann-Roch and duality theorems

The research was partly supported by the NSF grant DMS-9204940.     

Artin-Schreier extensions in NIP and simple fields

We show that NIP fields have no Artin-Schreier extension, and that simple fields have only a finite number of them.